A fault may be considered a finite complex three-dimensional surface discontinuity in a volume of earth or rock. Fractures, such as joints, veins, dikes, pressure solution seams with stylolites, and so forth, may be propagated intentionally, to increase permeability in formations such as shale, in which optimizing the number, placement, and size of fractures in the formation increases the yield of resources like shale gas.
Stress, in continuum mechanics, may be considered a measure of the internal forces acting within a volume. Such stress may be defined as a measure of the average force per unit area at a surface within the volume on which internal forces act. The internal forces are typically produced between the particles in the volume as a reaction to external forces applied on the volume.
Understanding the origin and evolution of faults and the tectonic history of faulted regions can be accomplished by relating fault orientation, slip direction, geologic and geodetic data to the state of stress in the earth's crust. In conventional inverse problems, the directions of the remote principal stresses and a ratio of their magnitudes are constrained by analyzing field data on fault orientations and slip directions as inferred from artifacts such as striations on exposed fault surfaces.
Conventional methods for stress inversion, using measured striations and/or throw on faults, are mainly based on the assumptions that the stress field is uniform within the rock mass embedding the faults (assuming no perturbed stress field), and that the slip on faults has the same direction and sense as the resolved far field stress on the fault plane. However, it has been shown that slip directions are affected by: anisotropy in fault compliance caused by irregular tip-line geometry; anisotropy in fault friction (surface corrugations); heterogeneity in host rock stiffness; and perturbation of the local stress field mainly due to mechanical interactions of adjacent faults. Mechanical interactions due to complex faults geometry in heterogeneous media should be taken into account while doing the stress inversion. By doing so, determining the parameters of such paleostress in the presence of multiple interacting faults requires running numerous simulations, and therefore an enormous amount of computation time in order to fit the observed data. The conventional parameters space has to be scanned for all possibilities, and for each simulation the model and the post-processes need to be recomputed.
Motion equations are typically not invoked while using conventional methods, and perturbations of the local stress field by fault slip are ignored. The mechanical role played by the faults in tectonic deformation is not explicitly included in such analyses. Still, a relatively full mechanical treatment is applied for conventional paleostress inversion. However, the results might be greatly improved if multiple types of data could be used to better constrain the inversion.